In school French classes, you learn that 'ici' is here and 'là' is there. Then you start using the language and you realize that's not even close. From experience it seems that the here/there distinction only holds true when two locations are being compared. Otherwise, it seems that 'là' is preferred for both English here and there in speech, while 'ici' tends to be used more for writing. But it can't be that simple. I went searching for an answer to this and found this question, but it only addresses the one case I mentioned above for one specific example and not the general usage difference between the two.

I am a native speaker, I was going to type an answer, and as I went along, I realized it is indeed very subtle and sometimes illogical. If I ask a kid to sit next to me to show something in a book I am holding, I would say "viens ici", but if I stretch out my arms to give him a hug, I would say "viens là"... and I could not explain why... I am quite sure it will also trigger some discussions on regional or even social differences..
– GregNov 16 '17 at 8:18

Là is deictically neutral, like doch in German if you're familiar with it, and making it the counterpart of there is a common error in teaching material, that reflects the etymology of là rather than its current usage. *There really corresponds to là-bas, and both là-bas and ici are only used when the distinction is important enough for it to be explicitly marked. In all other cases, là is used. The same loss of deictic contrast occurs with the enclitic demonstratives -ci and -là, with the second being systematically preferred, except for temporal deixis, where the contrast
– Eau qui dortNov 16 '17 at 17:21

4 Answers
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An important aspect of demonstratives is that of spatial deixis. Deixis marks the relationship of something to a point of reference, distance in the case of spatial deixis.

In English, here and there denote the spatial distance in relation to the speaker, the first proximal (near to the speaker), the second distal (far from the speaker). Likewise this/these and that/those. This is not the only possible deictic system a language can have, for example:

the tripartite ko-, so- and a- in Japanese, indicating respectively nearness to the speaker, nearness to the interlocutor and distance from both.

The tripartite seo, sin, siúd in Irish has proximal, medial and distal meanings (i.e. this, that near and that yonder)

The quadripartite i- (here) e- (there nearby), a- (there that I can see), u- (there that I can't see)

French is often described in paedagogical materials as having a system similar to that of English, with ici being the proximal demonstrative adverb and là being its distal counterpart, but as you've noticed là is used much more often than ici, and in reference to both proximal and distal elements.

The truth is that while such a spatial deixis contrast used to exist in Middle French, it has weakened to the point of near-disappearance in the modern language.

Among the language of the world, Modern French is unusual in not making a spatial deictic distinction in its demonstrative adverbs. Of the 234 languages surveyed by the World Atlas of Language Structures, only 7 share this feature.

The evolution of spatial deixis in French

So how did this oddity develop?

Looking back at the history of the French language, one can remark a constant weakening of its demonstrative system.

Latin had a system similar to that of Japanese, with hic (near the speaker), iste (near the hearer) and ille (far from both).

This system collapsed to a two-way distinction in the ancestor of French, Romanian and most Italo-Romance languages, but not in every other Romance variety (cf. Spanish este, ese and aquel). Reinforced forms of the old demonstratives were used in Old French to show proximal deixis ((i)cist, from ecce iste) and distal deixis ((i)cil, from ecce ille). Those words could be used as determiners and pronouns, but not adverbs (the ancestors of ici and là, (i)ci and la, from ecce hic and illac, were used).

A new merger started with the masculine plural forms of cist and cil, which by Middle French had both evolved to cez. This prompted the creation of an analogical fused singular ce. Those words survive to Modern French as the demonstrative determiner ce(s). A new series of demonstrative pronouns was then created from ce + the tonic personal pronoun (i.e. ce+lui = celui).

This left French without a deictic distinction in either its demonstrative pronouns or its demonstrative determiners. To repair the system, the sole words that still showed a constrast -(i)ci and là- were recruited to optionally reinforce the other demonstratives:

Ce+ci/là -> ceci, cela

Cette chose+ci/là -> cette chose-ci, cette chose-là

Ce+eux+ci/là > ceux-ci, ceux-là

This completely optional reinforcement further weakened the deictic contrast in the language. As it wasn't necessary in most contexts, this left the demonstrative adverbs as abnormally marked. This anomaly was rectified by recruiting là as an unmarked, deictically neutral demonstrative adverb.

To replace là as the optional distal demonstrative adverb, the more marked là-bas was in turn recruited, bringing the adverbs in line with the rest of the demonstrative system, with a normal, unmarked form, and an optional distal/proximal contrast. (Compare to English where there is no way not to indicate if something is far or near)

Spatial Deixis in Modern French

Sadly, the change outlined above was still in progress when French was standardised, leading to a certain confusion in both ESL and native manuals and differences between registers.

The generalized tendency is for the optional deictic contrast to weaken further, with old distal forms supplanting their proximal counterparts, as exemplified by ça supplanting both ceci and its progenitor cela as an inanimate demonstrative pronoun. Likewise the enclitic demonstrative -là, tends to be being systematically preferred to -ci and voilà to voici.

To come back to your main question after this long explanation, one uses là in most situations where the distinction isn't very important. Ici and là-bas are used when there is a risk of incomprehension, or when the distinction is important. This is highly dependent on the context you find yourself in as it relies on the speaker finding a deictic distinction important enough to include in their current speech act. It's thus difficult to give a systematic rule.

As an example, take "I come from (t)here". You'd say it as:

"Je viens de là" when you're showing the place on a map (you're equally far from all positions on the map, being a bird eye view observator) or if someone just mentioned your native town in a conversation (where you are, currently, in relation to this place doesn't matter to your present conversation)

"Je viens d'ici" when you want to mention that you've grown up in the town you're currently in (being in the town is important and relevant to the conversation)

"Je viens de là-bas" when you're pointing out the direction you just came from (that you came from somewhere away from your current position is relevant)

A note on temporal deixis

Contrarily to everything I've just written about spatial deixis, temporal deixis remains strong and stable:

Ce mois-ci can only mean "this month we're in" and ce mois-là designates every other month. While it's perfectly possible to say "ce PC-là" to speak of the computer you're sitting in front of right now, it's not possible to say "cette année-là" to mean the current year. The unmarked "ce mois" is normally understood as synonymous with "ce mois-ci".

Là is also used with a temporal meaning to indicate the present instant, translatable as "right now".

Far better than I expected, and among the rare truly riveting linguistic texts :)
– TheEnvironmentalistNov 17 '17 at 4:05

Very good answer, thank you. I don't think that I would use “Je viens de là” if someone mentioned my hometown, though, but rather “je viens de là-bas”, and I am rather ambivalent on the map example, too.
– Evpok♦Nov 17 '17 at 11:08

@Evpok That's interesting. Do you mean you'd use ici or là-bas with the map?
– Eau qui dortNov 18 '17 at 16:19

I don't see the point of these examples. There isn't a choice with là où. And it's the same en English, since it would be translated to where.
– Stéphane Gimenez♦Nov 16 '17 at 15:48

I really wasn't asking about the direct translation of là and ici into here/there, though I definitely appreciate the input. I was looking for when, intuitively, each would be used in speech and text, without any particular emphasis on English translation. In other words, in what situations would one use là, and in what situations would one use ici?
– TheEnvironmentalistNov 16 '17 at 17:11

First the etymology, ici is a contraction of ecce hic (lat.), meaning basically "this very place",Là comes from illac, which can be an adverb of place, and can also be a demonstrative, like "that" in english.

So the original opposition was between ci (hic) and là (illac), but "ci" is just not used anymore except with demonstrative "celui-ci" (this one) opposed to "celui-là" (that one).

Ici as a reinforced form : "Je suis ici chez moi !" (a way of telling someone that you're the king in you own house) can't be replaced by là. (It's the closest use to its etymology)

As an actual adverb of place, it will be used to distinguish a place from an other (with or without distance between them) : "Ici j'ai une main gauche, là une main droite." (I know, ludicrous example, but it's clear).

It will always be used as a starting point with d' : D'ici (où je suis) à Paris, il y a trois heures de route.

In any other case, even if It should be more logical to use it, ici tends to be replaced with là, it's the current evolution of french.